Exponential Functions (Graphs)

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises sharply as x increases, starting from a point above the x-axis (if a > 0) and approaching the x-axis but never touching it.

Tags

CCSS.HSF-IF.C.7E

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function falls sharply as x increases, starting from a point above the x-axis and approaching the x-axis but never touching it.

Tags

CCSS.HSF-IF.C.7E

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the point (0, a), where 'a' is the initial value of the function.

Tags

CCSS.HSF-IF.C.7E

Front

How can you identify exponential growth from a graph?

Back

Exponential growth can be identified by a graph that rises steeply to the right, indicating that the function's value increases rapidly as x increases.

Tags

CCSS.HSF-IF.C.7E

Front

How can you identify exponential decay from a graph?

Back

Exponential decay can be identified by a graph that falls steeply to the right, indicating that the function's value decreases rapidly as x increases.

Tags

CCSS.HSF-IF.C.7E

Front

What is the base in an exponential function?

Back

The base in an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

What does it mean if an exponential function has a base less than 1?

Back

If an exponential function has a base less than 1, it represents exponential decay, meaning the function's value decreases as x increases.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean if an exponential function has a base greater than 1?

Back

If an exponential function has a base greater than 1, it represents exponential growth, meaning the function's value increases as x increases.

Tags

CCSS.HSF-IF.C.8B